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Simplifying 6(5z + -1) + -4(z + 5) = 3(z + 1) Reorder the terms: 6(-1 + 5z) + -4(z + 5) = 3(z + 1) (-1 * 6 + 5z * 6) + -4(z + 5) = 3(z + 1) (-6 + 30z) + -4(z + 5) = 3(z + 1) Reorder the terms: -6 + 30z + -4(5 + z) = 3(z + 1) -6 + 30z + (5 * -4 + z * -4) = 3(z + 1) -6 + 30z + (-20 + -4z) = 3(z + 1) Reorder the terms: -6 + -20 + 30z + -4z = 3(z + 1) Combine like terms: -6 + -20 = -26 -26 + 30z + -4z = 3(z + 1) Combine like terms: 30z + -4z = 26z -26 + 26z = 3(z + 1) Reorder the terms: -26 + 26z = 3(1 + z) -26 + 26z = (1 * 3 + z * 3) -26 + 26z = (3 + 3z) Solving -26 + 26z = 3 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -26 + 26z + -3z = 3 + 3z + -3z Combine like terms: 26z + -3z = 23z -26 + 23z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -26 + 23z = 3 + 0 -26 + 23z = 3 Add '26' to each side of the equation. -26 + 26 + 23z = 3 + 26 Combine like terms: -26 + 26 = 0 0 + 23z = 3 + 26 23z = 3 + 26 Combine like terms: 3 + 26 = 29 23z = 29 Divide each side by '23'. z = 1.260869565 Simplifying z = 1.260869565
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